benderscript/float_parsers

Scripts for analyzing floating number representations

Float Parsers

http://github.com/goerz/float_parsers

Author: Michael Goerz

Float Parsers is a collection of scripts for analyzing single and double precision floating point numbers in their exact binary representation.

Given a representation (as a hex string) or a float value (as a string like "1.2" or "-2.3456e-192") they decompose the binary representation into sign, exponent, and mantissa, and print out this information along with the exact decimal the binary representation corresponds to according to the floating point model.

To understand the details of the binary representation for single and double precision floats, look at the Wikipedia articles for the Double precision floating-point format and Single precision floating-point format.

A similar online tool for double precision floats is available at www.binaryconvert.com (also single precision and others).

Install

Store the scripts anywhere in your $PATH.

Usage

Some usage examples for the parse_dp_float.py (double precision) script:

$> ./parse_dp_float.py 1.2

Bytes         = 0x3ff3333333333333
Float         = 1.200000000000000e+00
Sign          = +1
Exponent      = 0x3ff = 1023 (bias 1023)
Mantissa      = 0x3333333333333
Exact Decimal = + 2^(0) * (0x13333333333333 * 2^(-52))
              = 1.1999999999999999555910790149937383830547332763671875

You can give multiple values at once, and "special" values are handled properly:

$>./parse_dp_float.py -- "7fef ffff ffff ffff"  "8000 0000 0000 0000" "0.33333" "fff0 0000 0000 0000"

Bytes         = 0x7fefffffffffffff
Float         = 1.797693134862316e+308
Sign          = +1
Exponent      = 0x7fe = 2046 (bias 1023)
Mantissa      = 0xfffffffffffff
Exact Decimal = + 2^(1023) * (0x1fffffffffffff * 2^(-52))
              = 17976931348623157081452742373170435679807056752584499659891
                74768031572607800285387605895586327668781715404589535143824
                64234321326889464182768467546703537516986049910576551282076
                24549009038932894407586850845513394230458323690322294816580
                85593321233482747978262041447231687381771809192998812504040
                26184124858368

Bytes         = 0x8000000000000000
Float         = -0.000000000000000e+00
Sign          = -1
Exponent      = 0x0 (Special: Zero/Subnormal)
Mantissa      = 0x0
Exact Decimal = -0

Bytes         = 0x3fd555475a31a4be
Float         = 3.333300000000000e-01
Sign          = +1
Exponent      = 0x3fd = 1021 (bias 1023)
Mantissa      = 0x555475a31a4be
Exact Decimal = + 2^(-2) * (0x1555475a31a4be * 2^(-52))
              = 0.33333000000000001517008740847813896834850311279296875

Bytes         = 0xfff0000000000000
Float         = -inf
Sign          = -1
Exponent      = 0x7ff (Special: NaN/Infinity)
Mantissa      = 0x0
Exact Decimal = -Infinity

You can also get a shortened output, and format floats arbitrarily:

$> ./parse_dp_float.py --float --format='%.5f' "3fd5 5555 5555 5555"
0.33333

The single precision script works completely equivalently:

$> ./parse_sp_float.py "ff80 0000" c0000000 0.3333333333333333

Bytes         = 0xff800000
Float         = -inf
Sign          = -1
Exponent      = 0xff (Special: NaN/Infinity)
Mantissa      = 0x0
Exact Decimal = -Infinity

Bytes         = 0xc0000000
Float         = -2.000000e+00
Sign          = -1
Exponent      = 0x80 = 128 (bias 127)
Mantissa      = 0x0
Exact Decimal = -2

Bytes         = 0x3eaaaaab
Float         = 3.333333e-01
Sign          = +1
Exponent      = 0x7d = 125 (bias 127)
Mantissa      = 0x200001
Exact Decimal = 0.3333333432674407958984375